Following discoveries of blue ice areas in Greenland resembling meteorite-bearing blue ice fields in Antarctica, a surface search of several of the most promising sites was carried out in August 2003. The ice fields are located in Kong Christian X Land, in northeastern Greenland around 74 degrees N at elevations between 2100 and 2400 in. No meteorites were found in any of the localities that were searched. Evidence of occasional significant melting (filled crevasses and melt sheets) suggest that summer temperatures are sometimes high enough that dark rocks, like meteorites, can melt through the upper layers of ice. Small terrestrial rocks and cryogenite were found down to 50 cm, below the ice surface. Meter-sized terrestrial rocks were found on top of the ice downstream from nunataks. These rocks shade the ice below, and since they were apparently too massive to warm up during warm days, they remained at the surface as the surrounding ice ablated away. Our findings strongly suggest that Greenland is currently unlikely to harbor significant meteorite concentrations on blue ice fields.